BMW Insured Warranty Quandry

[CargoesVroom]

Hello guys, I'm hoping that you can help me with this situation I find myself in.

I bought a X5 M in 2018, at the time the car was already 8 years old, has had 3 previous owners. I purchased a BMW Insured Warranty and have been paying ever since (I know, I know, don't come at me for this, please).

Car has done 138,000 miles so far. I have kept on top of servicing the car regularly and only at the BMW dealership, an issue has come up with Engine Failure, Reduced Power. Upon diagnosis, the dealer said that even though the root cause is a single failed fuel injector , and this is a named component on my warranty, BMW Warranty needs me to grant the dealer permission to strip the car to replace the faulty injector. The problem is that the dealer is stating that the cost of stripping the car will be £6000, before any repairs is carried out, and potentially if they find that gaskets, valves , bolts etc needs replacing during the stripping process, I will incurr this cost too.

Did I mention that this issue has been a long running , recurring one, where we have changed quite a lot in the car, I'm talking about water pump, turbo pump, transmission fluid, ignition coils, spark plugs, all under warranty albeit having to pay £250 excess each time.

Can you offer some advice on this? I really love this car and I do not want to buy another one as I am content just need this issue fixed. Is BMW Warranty or the dealer trying to fleece me on this?